Difference between revisions of "Nine point circle"
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The '''nine point circle''' (also known as ''Euler's circle'' or ''Feuerbach's circle'') of a given [[triangle]] is a circle which passes through 9 "significant" points: | The '''nine point circle''' (also known as ''Euler's circle'' or ''Feuerbach's circle'') of a given [[triangle]] is a circle which passes through 9 "significant" points: | ||
| − | + | * The three feet of the [[altitude]]s of the triangle. | |
| − | + | * The three [[midpoint]]s of the [[edge]]s of the triangle. | |
| − | + | * The three midpoints of the segments joining the [[vertex | vertices]] of the triangle to its [[orthocenter]]. (These points are sometimes known as the [[Euler point]]s of the triangle.) | |
| − | That such a circle exists is a non-trivial theorem of [[ | + | That such a circle exists is a non-trivial theorem of Euclidean [[geometry]]. |
The center of the nine point circle is the [[nine-point center]] and is usually denoted <math>N</math>. | The center of the nine point circle is the [[nine-point center]] and is usually denoted <math>N</math>. | ||
{{stub}} | {{stub}} | ||
| − | + | [[Category:Definition]] | |
Revision as of 11:47, 6 July 2007
The nine point circle (also known as Euler's circle or Feuerbach's circle) of a given triangle is a circle which passes through 9 "significant" points:
- The three feet of the altitudes of the triangle.
- The three midpoints of the edges of the triangle.
- The three midpoints of the segments joining the vertices of the triangle to its orthocenter. (These points are sometimes known as the Euler points of the triangle.)
That such a circle exists is a non-trivial theorem of Euclidean geometry.
The center of the nine point circle is the nine-point center and is usually denoted 
.
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